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Unsupervised curve clustering using B-splines. (English) Zbl 1039.91067
The model of observations is $$y_j^i=G^i(x_j^i)+\varepsilon_J^i$$, where $$G^i$$, $$i=1,\dots,n$$ is the $$i$$-th experimental curve, $$(y_j^i,x_j^i)$$ are observations, $$\varepsilon_j^i$$ are i.i.d. errors. The authors propose to fit $$G^i$$ by B-splines and then to partition the coefficient vectors $$\beta^i$$ of these splines by $$k$$-means clustering. It is shown that under suitable assumptions this procedure is consistent, i.e. the sequence of the cluster centres (means) tends to the minimizer of the sum of $$L_2$$ distances between $$G^i$$ and the nearest centre. This technique is applied to a data on cheese production.

##### MSC:
 91C20 Clustering in the social and behavioral sciences 62G08 Nonparametric regression and quantile regression
##### Keywords:
$$k$$-means clustering; consistency; epi-convergence
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